The Atomic Nucleus as a Relativistic System

by Savushkin, L. N.; Toki, H.

• ISBN13: 9783540404927
• ISBN10: 3540404929
• Format: Hardcover
• Copyright: 2004-03-19
• Publisher: Springer Verlag

Summary

Relativity plays an important role in atomic nuclei, and, since the early 1970s, there has been increasing interest in, and literature on, the nucleus as a relativistic system. In fact, the relativistic treatment provides a powerful method to describe nuclear structure and reactions. It is thus an ideal time to collect and review the important landmarks in this book. Directed to advanced students and researchers, it explains both the underlying relativistic theory and compares predictions with actual experiments.

Table of Contents

1 Introduction	1	(6)
2 Relativistic Quantum Mechanics and Fields	7	(18)
2.1 The Dirac Equation	7	(1)
2.2 Solutions for Free Particles	8	(3)
2.3 Relativistic Free-Field Theories	11	(9)
2.3.1 Real Scalar Field	12	(1)
2.3.2 Vector Field	13	(1)
2.3.3 Electromagnetic Field	13	(1)
2.3.4 Spinor Dirac Field	14	(1)
2.3.5 Real Scalar Field with Quartic Self-Interaction	14	(6)
2.4 The Dirac Equation in a Central Potential	20	(5)
3 Basic Features of the Meson Theory of Nucleon-Nucleon Interactions	25	(14)
3.1 One-Boson Exchange Potentials in Configuration Space	25	(7)
3.2 One-Boson Exchange Potentials in Momentum Space	32	(7)
4 The Relativistic Mean-Field Approximation for Nuclear Structure	39	(36)
4.1 General Characteristics of the Relativistic Framework	39	(9)
4.1.1 Large Scalar and Vector Fields	39	(1)
4.1.2 Spin-Orbit Force	40	(1)
4.1.3 Saturation	40	(8)
4.2 Relativistic Mean-Field Approximation for Finite Nuclei	48	(4)
4.3 Relation of the RMF Model to the Skyrme-Hartree-Fock Approach	52	(10)
4.4 Renormalization of the Kinetic Energy to Obtain Saturation in Nuclear Matter	62	(2)
4.5 Relativistic Mean-Field Approximation for Deformed Nuclei	64	(3)
4.6 Optimal Parameter Sets for the Relativistic Mean-Field Model	67	(8)
5 Electromagnetic Interactions of Nucleons in the Relativistic Framework	75	(14)
5.1 The Vector Dominance Model and the Nuclear Coulomb Potential	75	(7)
5.1.1 Results of Calculations	80	(2)
5.2 Nuclear Magnetic Moments in the Relativistic Approach	82	(7)
6 The Relativistic Approach to Nucleon-Nucleus Scattering	89	(10)
6.1 Energy Dependence of the Real Part of the Optical Potential	89	(3)
6.2 Coulomb-Nuclear Interference Effects in Nucleon-Nucleus Scattering	92	(2)
6.3 Relativistic Impulse Approximation	94	(2)
6.4 p-Nucleus Scattering	96	(3)
7 Pion Dynamics and Chiral Symmetry	99	(38)
7.1 Pionic Excitations in Nuclear Matter	99	(2)
7.2 Equations of Motion for a Pion Field in a Nuclear Medium	101	(3)
7.3 Pionic Polarization in Infinite Nuclear Matter	104	(3)
7.4 Contribution of the Δ33 Resonance to the Pion Polarization Operator	107	(6)
7.5 Basic Equations of the Linear σ and σ-ω Models	113	(9)
7.6 Chiral σ-ω Model for Finite Nuclei	122	(3)
7.7 Effective Gauge-Invariant Nuclear Lagrangian	125	(5)
7.8 Mean-Field Results for Nuclear Matter and Finite Nuclei	130	(7)
8 The Relativistic Hartree-Fock Approach	137	(36)
8.1 The Relativistic Hartree-Fock Lagrangian	137	(4)
8.2 The Relativistic Hartree-Fock Approach for Symmetric Nuclear Matter	141	(5)
8.3 The Relativistic Hartree-Fock Approach for Finite Nuclei	146	(2)
8.4 Determination of Parameters and Numerical Results	148	(6)
8.5 The Relativistic Hartree-Fock Approach with Meson Self-Coupling Terms	154	(6)
8.6 Spin-Orbit Interaction	160	(5)
8.7 Pseudospin as a Relativistic Symmetry	165	(8)
9 Brueckner-Hartree-Fock Methods for Nuclear Matter and Finite Nuclei	173	(28)
9.1 The Brueckner-Hartree-Fock Approach	173	(2)
9.2 The Brueckner-Bethe-Goldstone Method for Internucleon Correlations	175	(7)
9.3 Δ-Isobar for Nuclear Interactions and Nuclear Structure	182	(5)
9.4 Relativistic Extension of the BHF Theory for Nuclear Matter	187	(7)
9.5 Finite Nuclei	194	(7)
10 Excited Nuclear States in the Relativistic RPA Method	201	(18)
10.1 RRPA Method for Nuclear Matter and Finite Nuclei	201	(2)
10.2 RRPA with Nonlinear Interactions for Giant Resonances	203	(3)
10.3 Construction of the Meson Propagators	206	(2)
10.4 Results for Collective States and Giant Resonances	208	(8)
10.5 Cranked Relativistic Mean-Field Theory	216	(3)
11 The Equation of State of Nuclear Matter for Supernovas and Neutron Stars	219	(20)
11.1 Thomas-Fermi Method for Nonuniform Matter	219	(4)
11.2 Equation of State of Nuclear Matter	223	(9)
11.3 Neutron Star Matter and Neutron Star Profiles	232	(7)
12 Alternative Relativistic Models	239	(22)
12.1 Quark-Meson Coupling Models	239	(7)
12.2 The Relativistic Point-Coupling Model	246	(7)
12.3 Scalar Derivative Coupling Models	253	(8)
13 Some Recent Applications of Relativistic Nuclear Theory	261	(28)
13.1 Mean Fields in Colliding Nuclear Matter	261	(2)
13.2 Hartree-Fock-Bogoliubov Approximation	263	(3)
13.3 Spin-Orbit Splitting for Single-Particle and Single-Hole Energies	266	(1)
13.4 The Anomalous Kink in the Isotope Shifts of Pb Nuclei	267	(1)
13.5 Electroweak Interactions in Nuclei in the Relativistic Framework	268	(2)
13.6 Hypernuclei in the Relativistic Framework	270	(1)
13.7 Theoretical Analysis of A(e, e'p)B Reactions	271	(1)
13.8 Exclusive Pion Production in Nucleon-Nucleus Scattering	272	(2)
13.9 The Role of Relativity in Few-Body Systems	274	(2)
13.10 Systematic Study of Even-Even Nuclei up to the Drip Lines	276	(3)
13.11 Exotic Nuclei and Superheavy Nuclei	279	(2)
13.12 Dilepton Production by Bremsstrahlung of Meson Fields in Nuclear Collisions	281	(1)
13.13 (p, n) Spin Experiments and Relativity in Nuclear Physics	282	(2)
13.14 Role of Currents (ω and ρ Fields)	284	(1)
13.15 Fission Barriers	285	(1)
13.16 Chiral Dynamics and Saturation of Nuclear Structure	286	(3)
14 Summary and Outlook	289	(4)
A Appendices	293	(30)
A.1 Four-Dimensional Notation and the Dirac Matrices	293	(3)
A.2 Properties of the Ground State of Nuclear Matter in the Walecka Model	296	(1)
A.3 General Form of Local Dirac Equation	297	(2)
A.4 Equivalent Local Dirac Nuclear Models	299	(1)
A.5 Nucleon Effective Mass in the Nuclear Medium	300	(2)
A.6 Radial Equations for the Upper and Lower Components G(r) and F(r)	302	(2)
A.7 Boundary Conditions for Wave Functions and Meson Potentials	304	(1)
A.8 Generalized Weinberg Transformation	305	(1)
A.9 Expansions of the Vertex Functions for Various Mesons	306	(1)
A.10 Globally Chirally Invariant Lagrangian for the Model with an Axial Meson	307	(2)
A.11 Direct and Exchange Matrix Elements for the Two-Body Spin-Orbit Force	309	(9)
A.12 Hartree-Fock Procedure for the Point-Coupling Model	318	(5)
References	323	(24)
Index	347